We measure tunneling through a single quantum level in a carbon nanotube quantum dot connected to resistive metal leads. For the electrons tunneling to/from the nanotube, the leads serve as a dissipative environment, which suppresses the tunneling rate. In the regime of sequential tunneling, the height of the single-electron conductance peaks increases as the temperature is lowered, although it scales more weakly than the conventional T-1. In the resonant tunneling regime (temperature smaller than the level width), the peak width approaches saturation, while the peak height starts to decrease. Overall, the peak height shows a nonmonotonic temperature dependence. We associate this unusual behavior with the transition from the sequential to the resonant tunneling through a single quantum level in a dissipative environment. © 2009 The American Physical Society.